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THE DENSITY OF SUBGROUP INDICES

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  01 October 2008

ANER SHALEV
ANER SHALEV*
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel (email: [email protected])
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Abstract

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For a group G and a real number x≥1 we let sG(x) denote the number of indices ≤x of subgroups of G. We call the function sG the subgroup density of G, and initiate a study of its asymptotics and its relation to the algebraic structure of G. We also count indices ≤x of maximal subgroups of G, and relate it to symmetric and alternating quotients of G.

Keywords

subgroup indicesspecial linear groups

MSC classification

Secondary: 20E07: Subgroup theorems; subgroup growth 20F69: Asymptotic properties of groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 2 , October 2008 , pp. 257 - 267
Copyright
Copyright © 2008 Australian Mathematical Society

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